Question

A box contains 3 white and 2 red balls. If the first drawn ball was not replaced then the probability that the second drawing ball will be red is

• A. $\frac{8}{25}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{21}{35}$

Answer 1

The correct option is B $\frac{2}{5}$

Let A $\equiv$ the event that drawn ball is white.
B $\equiv$ the event that drawn ball is red.
There are two mutually exclusive cases of the required event: WR and RR
Now $P\left(WR\right)=P\left(W\right)P\left(\frac{R}{W}\right)=\frac{3}{5}.\frac{2}{4}=\frac{6}{20}$
$P\left(RR\right)=P\left(R\right)P\left(\frac{R}{R}\right)=\frac{2}{5}.\frac{1}{4}=\frac{2}{20}$
$\therefore$ Required Probability=P(WR+RR)=P(WR)+P(RR)
$=\frac{6}{20}+\frac{2}{20}=\frac{8}{20}=\frac{2}{5}$